SOLUTION: A mutual fund has 20 stocks in its portfolio. On a given day 3 stocks move up, 14 stay the same and 3 move down. In how many ways could this happen?

Algebra ->  Permutations -> SOLUTION: A mutual fund has 20 stocks in its portfolio. On a given day 3 stocks move up, 14 stay the same and 3 move down. In how many ways could this happen?       Log On


   



Question 1153122: A mutual fund has 20 stocks in its portfolio. On a given day 3 stocks move up, 14 stay the same and 3 move down. In how many ways could this happen?

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

I do not like very much, when the problem is formulated this way, asking "could this happen",

because then INEVITABLY I should reformulate it, explaining what this "THIS" means, 

making the job of the author of the post, to whom it is his direct duty and responsibility.



The problem asks, in how many ways 3 items can be selected from 20 items, and in how many ways then 
14 items can be selected from the remaining 20-3 = 17 items.



The answer is:  in  C%5B20%5D%5E3.C%5B17%5D%5E14 ways = %2820%2A19%2A18%29%2F%281%2A2%2A3%29.%2817%2A16%2A15%29%2F%281%2A2%2A3%29 different ways.



Use your calculator.